Giant ferroelectric polarization in a bilayer graphene heterostructure

At the interface of van der Waals heterostructures, the crystal symmetry and the electronic structure can be reconstructed, giving rise to physical properties superior to or absent in parent materials. Here by studying a Bernal bilayer graphene moiré superlattice encapsulated by 30°-twisted boron nitride flakes, we report an unprecedented ferroelectric polarization with the areal charge density up to 1013 cm−2, which is far beyond the capacity of a moiré band. The translated polarization ~5 pC m−1 is among the highest interfacial ferroelectrics engineered by artificially stacking van der Waals crystals. The gate-specific ferroelectricity and co-occurring anomalous screening are further visualized via Landau levels, and remain robust for Fermi surfaces outside moiré bands, confirming their independence on correlated electrons. We also find that the gate-specific resistance hysteresis loops could be turned off by the other gate, providing an additional control knob. Furthermore, the ferroelectric switching can be applied to intrinsic properties such as topological valley current. Overall, the gate-specific ferroelectricity with strongly enhanced charge polarization may encourage more explorations to optimize and enrich this novel class of ferroelectricity, and promote device applications for ferroelectric switching of various quantum phenomena.

D1, the larger scanning range leads to an unstable hysteresis and the states try to approach the stable states with anomalous screening. In opposite, for D2 a smaller range of the trivial gate (to be specific, on the negative side) turns out to be essential to eliminate the hysteresis (partially). More investigation is needed to explain the discrepancy on a quantitative level, which is extremely important to explore the switching functionality of a hysteretic device.

More control devices
To pin down the critical configuration for hysteretic behaviors, three types of devices were designed and prepared. Here we define the angle between graphene and the top (bottom) gate as θt (θb), and the angle between two hBN as Θ. As seen from Table S1, both top and bottom gates have ~0º alignment with the bilayer graphene in DG4 and DG6. However, neither hysteresis nor anomalous screening could be observed, despite the formation of a moiré superlattice. In contrast, when one of the gates is marginally twisted by 30º as in D2 and D1, hysteresis and anomalous screening immediately take place regardless of moiré features. It's important to stress that a device without moiré features does not mean the absence of moiré superlattices: the twisted angle that could be detected by electric measurement for our devices is less than ~2 degrees, due to the typical breakdown voltage of hBN flakes. For instances, in D2 (this study), the twist angle is around 2.7 degrees determined by optical measurement, but moiré features are in lack in resistance measurements. In such a device, a moiré superlattice is still present, although with a shorter superlattice constant and probably without electronic correlation.
In addition, to check whether the 30º twisted interface between graphene and hBN is the key factor, θb was set to be far away from symmetric axes while keeping θt ~30º (DG8, 9 and 10). As expected, there was no moiré superlattice formed. Neither were hysteresis and anomalous screening. Overall, we can tentatively conclude that small-angle twisted interfaces and thus the resultant moiré superlattice are still essential to observe ferroelectricity in graphene heterostructures.

Discussion about the mechanism
Generally speaking, ferroelectricity could originate from pure electron dynamics or spontaneous lattice distortion. For the device studied in this work, there are only crystallographically aligned bilayer graphene and hBN flakes, thus we discuss all possible electron-and/or lattice-driven mechanisms in terms of constituent layers and the interface. a) Correlation induced interlayer charge transfer (within the bilayer graphene) In this scenario, the essential object is the bilayer graphene, while the hBN flakes merely provide a special electrostatic environment. The bilayer graphene, subjected to perpendicular electric fields and a periodic superlattice potential, is endowed with layer-polarized moiré bands, i.e., the electron and hole mini-bands reside in the bottom and top graphene, respectively. Electrons may exhibit strong correlation due to the narrow bandwidth of moiré bands. As shown in Fig. S20a, electrons firstly fill the valence band (the top layer in real space). Upon the band is half filled, the on-site energy U excludes double occupation within each moiré supercell, which is translated as band splitting in the momentum space. Compared with the energy gap Δ between conduction and valence bands, a larger U will result in prior population of the conduction band (the bottom layer in real space). In other words, electrons transfer from the top to the bottom layer, generating electric dipoles ordering between the two layers.
The above interlayer charge transfer model is able to qualitatively explain several key experimental observations, such as the difference between normal and special gates, the accompanied anomalous screening and so on. For the different gates, there may be only one hBN flake that forms a strong moiré pattern with graphene, whose corresponding min-band is narrow enough to introduce correlation for further Hubbard band splitting. Consequently, this gate behaves as a special gate and the other as a normal one. For the anomalous screening, during the process of band splitting, the gate voltage (of the special gate) needs to compensate the rising chemical potential, so that no additional carriers are introduced into the system, mimicking the 'stop-working' behavior. As a result, this scenario was previously believed to account for the moiré ferroelectricity, despite the lack of moiré features in experiments.
However, as pointed out in the manuscript, the basis of the above ICT modelcorrelated electronshas not been scrutinized yet. Our devices with clear moiré features severely contradict with the moiré physics on a quantitative level. Firstly, the amount of transferred electrons is found to depend on specific status of the device (Fig. 3 in main text), which can far exceed the capacity of a moiré band. Such a quantitative comparison was in lack in literatures due to the missing moiré features. Secondly, the concomitant anomalous screening can occur outside the moiré bands (on the electron and hole sides), i.e., within dispersive bands ( Fig. 2 in main text), which is against electronic correlation.
At last, we check the material dependence. Besides Bernal bilayer graphene, twisted bilayer graphene 4 and hBN intercalated bilayer graphene 3 also exhibit very similar ferroelectricity. The collection of these materials is actually very important to identify whether correlation is the key ingredient: While the former definitely has correlated electrons, the latter is expected to be free from electronic correlation. Therefore, graphene ferroelectricity seems to be independence of correlation, in line with our experimental results.
The new findings are in discrepancy with moiré bands of correlated electrons, challenging the ICT model.
Nevertheless, it does not mean that an electron-driven mechanism is invalid; some new mechanisms that induce interlayer charge transfer is in demand b) Sliding ferroelectricity (at the interface between graphene and hBN) It is also possible that the ferroelectricity stems from lattice distortion, just like almost all conventional ferroelectric materials. Following the well-established sliding ferroelectricity, we plot a single graphene layer and the crystallographically aligned hBN in Fig. S20b. Note that the outer layer of graphene is omitted because it is much less influenced by the hBN owing to a large distance.
Inside a moiré supercell, there are two polar states at the graphene/hBN interface 5 : when half of the C atoms of the graphene layer locate right over the N atoms of hBN layer, the π electron cloud of the C atoms will be repelled by the N atoms with negative charge, giving rise to a vertical polarization downwards; in contrast, when half of the C atoms of the graphene layer locate right over the B atoms, the π electron cloud of the C atoms will be attracted and prolonged by the B atoms with positive charge, giving rise to a vertical polarization upwards. Note that when both B and N are overlaid by C atoms, the polarization is averaged out over the unit cell of graphene.
Although the two polar states could cancel each other over a moiré supercell, untwisted graphene/hBN interface may also exhibit ferroelectricity similar to the twisted bilayer hBN [6][7][8] , where the macroscopic polarization is switched by expanding/shrinking the area of polar states through domain wall motions. A theoretical justification is as follows: The density functional theory (DFT) calculation was carried out using the projector augmented wave (PAW) 9 scheme with the Perdew-Burke-Ernzerhof (PBE) functional of generalized gradient approximation (GGA) 10 method as implemented in the Vienna ab initio simulation package (VASP) 11,12 .
A plane wave cutoff of 750 eV was set in our calculations. K-point samplings of 12 × 12 × 1 was used.
optB88 level 13 was used in our calculations to taking into consideration of the van der Waal forces.
Atomic relaxation was performed until the force on each atom is smaller than 0.001 eV Å −1 , and the total energy change was less than 10 −6 eV. The vacuum spacing is set as at least 16 Å along the out-of-plane direction that is sufficiently large. The electric field action is equivalent to exerting equal and opposite displacements on the oppositely charged atoms carrying Born effective charges in the unit cell 14  As shown in Fig. S21b, it's obvious that the energy of AB-stacking and BA-stacking is different under the same electric field. When the electric field is small, the energy of AB-stacking is always lower than that of BA-stacking. So the area of AB stacking (blue color in the right insets) is greatly enlarged, and the BA stacking (red color in the right insets) shrinks simultaneously. When the upward electric field continues to increase, ΔU changes from a negative value to a positive value, which means the energy of AB-stacking becomes higher than that of BA-stacking. Hence the proportion of AB and BA stacking areas is reversed.
As also shown in previous DFT calculations 5 for graphene/hBN heterobilayer, the vertical polarizations for the AB stacking configurations with C atoms right over B atoms and C atoms over N atoms are respectively 1.5 pC/m and -0.33 pC/m, so the change in polarization after ferroelectric switching will be 1.83 pC/m, very close to that of MoS2 bilayer (0.97 pC/m-(-0.97 pC/m)=1.94 pC/m). We note that the electrically tunable lattice relaxation and resulting polarization for MoS2 bilayer have been simulated in a recent work 15 , where the domains with opposite polarizations relax unevenly (one enlarged and the other one squeezed) under external electric field, giving rise to non-zero net polarization.
It's important to stress that the above polarization is only valid in perpendicular electric fields. Once the electric field goes to zero, the polarization will diminish accordingly, in contrast to the definition of ferroelectricity where a polarized states survives without the presence of an electrical field. Defects, mislocations or strain disorders may preserve the polarization. However, such extrinsic factors are uncontrollable and highly depend on local configurations of a specific device, which are not in line with the uniform and repeatable ferroelectricity in experiments.
Moreover, this lattice driven mechanism is difficult to explain the accompanied anomalous screening at present. There is another indirect evidence. Since the switching between two polar states is via domain wall motion, the two polar states of practical samples may coexist. The coexistence can be directly observed by microscopic characterization ormore easilyby electrical measurements. For example, in twisted bilayer hBN double resistance peaks always appear in the phase diagram 6 , each of which represents either an upwards or downwards polar state. However, in our own samples and similar ones in the literature, such coexisting signals have never been observed. Instead, the polar states are verified to be quite uniform over the entire sample (Fig. S1c). All of these observations, although indirect, indicate that the graphene ferroelectricity is unlikely to be from a pure lattice distortion.

c) Sliding ferroelectricity (within hBN flakes)
The hBN flake may have stacking faults, invoking the sliding ferroelectricity naturally. However, this mechanism can be excluded completely. If such an imperfect hBN exists, both top and bottom hBN cut from the same thin crystal would enable hysteresis of resistivity, in direct contrast to the experimental results. Quantitatively, the polarized carrier in graphene is too large to be from sliding ferroelectricity in hBN because, as estimated in the manuscript, each layer of the hBN flake needs to be rhombohedrally stacked.
At last, we'd like to examine the origin of the special gate in this gate-specific ferroelectricity.
Corresponding to the two possible scenarios (subsections a and b in the above), the requirement of a special gate is as follows: (1) In the ICT model, a possible explanation of distinct functionality is that the top and bottom hBN does not provide equally strong periodic modulation of electrostatic potential. The stronger one that controls the Hubbard band splitting, anomalous screening and ferroelectricity, would act as a special gate. (2) In the scenario of sliding ferroelectricity, the special gate must be associated with a polarized interface between hBN and graphene, e.g., two polar states may arise due to the inequivalent influence of B and N on the π electron cloud of C atoms.
To summarize, our results demonstrate that neither the electron-driven ICT model nor the lattice-driven sliding ferroelectricity can solely explain all the observation, hence the combination of the two may be required for a complete model.      Fig. 2b. The blue and red curves denote, were there no relaxation, CNP positions of downward and upward scanning of Vt, respectively. However, the actual case is that the CNP position will move gradually towards the stable state, which is highlighted by an arrow. As the relaxation time is found to be distinct for Vt>0 and Vt<0 V, two representative points are selected for detailed characterization. b. The time dependent transfer characteristics at the point of Vt<0 V in zero fields. c. The evolution at the point of Vt>0 V. Note the magnetic field varies from 14 to -2 T, then increases to 10 T again.  originates from the narrow bandwidth of a moiré band. The band splitting may induce electron transfer from one layer to another, forming spatially ordered electric dipoles. b. Sliding ferroelectricity at the interface of graphene and hBN flakes. When the twist angle is small or even zero degrees, relatively large domains (~ several nanometers) of polar states can be formed. Around the red (blue) circle where C atoms locate just above N (B) atoms, the π electron cloud of C atoms is repelled (elongated) to form a polar state. In contrast, in the yellow circle such polarization cancels out over a unit cell of graphene.

Supplementary Tables
With external electric field along perpendicular direction, the domain areas may be enlarged or squeezed, leading to a net polarization over a moiré supercell. Schematics for the two polarized states in real space, where within a moiré supercell, blue (AB configuration) and red (BA configuration) regions are either enlarged or squeezed due to the positive/negative energy differences.